geomtery 8.1 The Pythagorean Theorem

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Transcript of geomtery 8.1 The Pythagorean Theorem

FinallyPythagorean Theorem8.1 The Pythagorean Theorem and its converseIn a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.Pythagorean TriplePythagorean Triple is a set of nonzero whole numbers a, b, and c that satisfy the Pythagorean Theorem equation. If you were on the beach on the southeast corner of a lake and wanted to go across to reach the northwest corner of a lake how far would you have to travel by boat if the northwest beach was 176 meters west and 330 meters north of the southeast beach.Find the length of the missing sideConverse of the Pythagorean theoremIf the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.What do you notice if you square the length of the sides of each triangle?(leg)(leg)(Hypotenuse)1.) 3, 4, 52.) 5, 12, 133.) 8, 15, 174.) 7, 24, 255.) 9, 40, 41Common Pythagorean Triple's1.)81517Is this a Pythagorean triple?If you multiply each number in a Pythagorean Triple by the same whole number, the 3 numbers that result also form a Pythagorean triple.1216203(4), 4(4), 5(4)2410X419XSolve for X.Find the value of x. Make sure to leave your answer in simplest radical form and not decimal.208__________________Ifthe triangle is acuteIfthe triangle is obtuseIs it a right triangle if the sides of a triangle are 8, 10, 12?Classify the triangle whose side lengths are 15, 7, 11.Pythagorean Theoremwhere C is the hypotenusewhere C is the hypotenuseX1.2.